It was recently found that the superconformal index has the information
about the entropy of the AdS blackhole [1]}.
In general, in the statistical derivation of
thermodynamic quantities
we first calculate the partition function
\(Z=\sum _kc_{E_k}q^{E_k}\) ,
where \(E_k\)  is energy levels, \(c_{E_k}\)  is the degeneracies
of each level, and \(q=e^{-1/T}\)  is the damping factor of the canonical
ansamble.
In the thermodynamic situation we can regard \(c_{E_k}\)  as
a smooth function \(c(E)\)  of the energy \(E\) , and
the summand \(c(E)q^E\)  of the partition function
has a sharp peak at \(E=E_0\) 
(Figure REF ).
From the summand \(c(E)q^E\)  and the coefficient \(c(E)\)  at the peak
we can determine the free energy \(F=-T\log (c(E_0)q^{E_0})\)  and
the entropy \(S=\log c(E_0)\) .
<FIGURE>